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Show that for any integer $n \geq 2$ the sum of the fractions $\frac{1}{a b}$, where $a$ and $b$ are relatively prime positive integers such that $a<b \leq n$ and $a+b>n$, equals $\frac{1}{2}$ (Integers $a$ and $b$ are called relatively prime if the greatest common divisor of $a$ and $b$ is 1.)
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